Unit 12 - Area Flashcards
What is the area of a parallelogram? (2)
- A = bh
- A = ab ⋅ sinc
What is the area of a triangle? (4)
- A = bh/2
- √s (s - a) (s - b) (s - c)
- (s/2)² √3
- (1/2) ab ⋅ sinc
What is the area of a trapezoid?
1/2 (b1 + b2) x h
What is the area of a rhombus/kite?
(diagonal 1 x diagonal 2) /2
What is Heron’s Formula? (3)
- Must be given all 3 side lengths
- Find Semi - Perimeter (Perimeter/2)
- √s (s - a) (s - b) (s - c)
What is the formula for finding the area of an equilateral triangle when given 1 side length?
A = (s/2)² √3
What is the formula for finding the area of a hexagon?
A = 6 (s/2)² √3
When do you know when to use (1/2) ab ⋅ sinc?
SAS
What is the equation for finding the area of a sector?
Area of Sector/πr2 = Measure of Central Angle/360
Definition of Apothem (3)
- Line segment
- Connects center of circle
- Perpendicular to a side of a polygon
Definition of Central Angle
Angle between two radii
What is the formula for percent error?
(|Measured - Actual|/Actual) x 100
What are the guidelines to classify figures as cylinders? (3)
- Planes are Parallel
- Planes are the Same Shape
- Planes are Connected with Infinite Amount of Segments
Definition of Oblique
Lateral edges are NOT perpendicular to the base
Definition of Prism
Cylinders with a Polygonal Base
What’s the relationship between cylinders and prisms?
All prisms are cylinders, but not all cylinders are prisms
What are the rules when naming cylinders? (3)
- Determine if Prism or Cylinder
- Determine if Oblique or Right
- Determine Shape of Plane (Based on # of Sides)
What is something to keep in mind when identifying the solid created through the rotation of 2D Shapes?
Circles will ALWAYS be involved
Definition of Cross Section
2D Shape created Plane Slices through Solid
Definition of Lateral Area
Sum of areas of the lateral faces of a cylinder.
Definition of Surface Area
- 2D measurement
- Sum of all areas of all faces (lateral and bases)
(LA + 2B)
What is the Lateral Area of a Right Circular Cylinder?
LA = 2πrh
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1. LA is just a rectangle
2. LA = lw
3. Length will be Height & Width will be Circumference
What is the SA of a Right Circular Cylinder? (2)
- LA + 2B
- 2πrh + 2 (πr²)
What is the SA of Rectangular Prism?
2lw + 2lh + 2wh
(Little WIlly Lost His White Hat)
How do you find the LA of a Triangular Prism?
LA = h (perimeter of base)
AREA OF TRIANGLE
1/2bh
AREA OF PARALLELOGRAM
- bh
- absinc
AREA OF KITE/RHOMBUS
(d1 x d2)/2
AREA OF TRIANGLE (SAS SETUP)
absinc/2
HERON’S FORMULA
s = p/2
√s (s-a) (s-b) (s-c)
AREA OF EQUILATERAL TRIANGLE
(s/2)²√3
AREA OF TRAPEZOID
1/2 (b1 + b2) h
AREA OF SIMILAR FIGURES
SA OF GENERAL CYLINDERS & PRISMS
LA + 2B
SA OF CIRCULAR CYLINDERS
2πrh (2πr)²
SA OF PYRAMIDS
LA + B
SA OF CIRCULAR CONES
πrL + πr²
AREA OF CIRCLE
πr²
SA OF RECTANGULAR PRISM
2 (lw + lh + wh)
SA OF CUBE
6s²
AREA OF SECTOR
As/πr² = m/360
LA OF PRISM
(Perimeter of Base) (Height of Prism)
PERCENT ERROR
(m-a)/a x 100
Definition of General Cone (3)
- Any region as a base (B)
- Point not on plane (P)
- Union of all segments between B and P
Definition of Circular Cone
General Cone with a Disk as a Base
Definition of Pyramid
General Cone with a Polygonal Base
Definition of Slant Height
Height of Each Lateral Face (𝓁)
What is the lateral area and surface area of a circular cone?
πr𝓁 = LA
πr𝓁 + πr² = SA
What is the height of a regular pyramid?
Altitude of pyramid goes from the vertex perpendicular to the center of the base
